Interference is a difficult problem in wireless communications. For instance, the capacity region of two-user Gaussian interference channels has been an open problem for over thirty years. Recently, there has been some progress in understanding interference and extensive studies have been done regarding interference alignment (IA) techniques. IA was proposed in M. A. Maddah-Ali, A. S. Motahari, and A. K. Khandani, “Signaling over MIMO multi-base systems-combination of multi-access and broadcast schemes,” in Proc. of IEEE ISIT, Page(s) 2104-2108, 2006., and M. A. Maddah-Ali, A. S. Motahari, and A. K. Khandani, “Communication over MIMO X channels: Interference alignment, decomposition, and performance analysis,” IEEE Trans. on Information Theory, Vol. 54, no. 8, Page(s) 3457-3470, August 2008, to reduce the effect of multi-user interference. IA was extended to deal with K pairs interference channels in Cadambe, V. R.; Jafar, S. A.; Shamai, S.; “Interference alignment and degrees of freedom of the K-user interference channel,” IEEE Trans. on Information Theory Vol. 54, No. 8, August 2008.
IA reduces the dimension of the aggregated interference by aligning interference from different transmitters into a lower dimension subspace at each receiver. Using infinite dimension extension on the time dimension (time selective fading), it has been shown that the IA can achieve the optimal Degrees-of-Freedom (DoF) of
  KN  2in K-pair multiple input multiple output (MIMO) ergodic interference channels with N antennas at each node.
One important challenge of IA schemes is the feasibility condition. For instance, the IA schemes in Cadambe require ((KN)2K2N2) dimensions of signal space to achieve the
  KN  2total DoF. To avoid such huge dimensions of signal space, some researchers have studied IA designs for quasi-static (or constant) MIMO interference channels. With limited signal space dimensions, the achievable DoF of each transmitter-receiver pair in MIMO interference channels is upper bounded by
            N      t        +          N      r            K    +    1  (where K is the number of transmitter-receiver pairs, Nt, Nr are the number of antennas at each transmitter and receiver, respectively). Unlike the time-selective or frequency-selective MIMO interference channels, total DoF of quasi-static MIMO interference channels do not scale with K.
Furthermore, for quasi-static MIMO channels, conventional IA might be infeasible depending on the system parameters. For example, it is conjectured in C. M. Yetis, T. Gou, S. A. Jafar, and A. H. Kayran, “On feasibility of interference alignment in MIMO interference networks,” IEE Trans. Signal Process., vol. 58, pp. 4771-4782, September 2010, that conventional IA on quasi-static MIMO (M transmit and N receive antennas) interference channels is not feasible to achieve a per user DoF greater than
            M      +      N              K      +      1        .As a result, IA alone is insufficient to eliminate all interference in quasi-static MIMO interference channels especially when K is large. For example, due to the fact that not all the interferers can be aligned at each receiver when K is large, there will be residual interference at the receiver.
The above-described deficiencies of conventional IA techniques are merely intended to provide an overview of some of problems of current technology, and are not intended to be exhaustive. Other problems with the state of the art, and corresponding benefits of some of the various non-limiting embodiments described herein, may become further apparent upon review of the following detailed description.